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Emergence of Coherence in the Charge-Density Wave State of 2H-Nbse2

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Emergence of Coherence in the Charge-Density Wave State of 2H-Nbse2 Emergence of coherence in the charge-density wave state of 2H-NbSe2 U. Chatterjee1,2*, J. Zhao2,3, M. Iavarone4, R. Di Capua4, J. P. Castellan1,5, G. Karapetrov6, C. D. Malliakas1,7, M. G. Kanatzidis1,7, H. Claus1, J. P. C. Ruff 8,9, F. 1, Weber 5, J. van Wezel1,10, J. C. Campuzano1,3, R. Osborn1, M. Randeria11, N. Trivedi11, M. R. Norman1 and S. Rosenkranz1* 1Materials Science Division, Argonne National Laboratory, , Argonne, IL 60439 USA. 2Department of Physics, University of Virginia, Charlottesville, VA 22904, USA. 3Department of Physics, University of Illinois at Chicago, Chicago, IL 60607, USA. 4Department of Physics, Temple University, Philadelphia, PA 19122, USA. 5Institute of Solid State Physics, Karlsruhe Institute of Technology, P.O. Box 3640, D-­‐76021 Karlsruhe, Germany. 6Department of Physics, Drexel University, Philadelphia, PA 19104, USA. 7Department of Chemistry, Northwestern University, Evanston, IL 60208, USA. 8Advanced Photon Source, Argonne National Laboratory, Argonne, , IL 60439 USA. 9CHESS, Cornell University, Ithaca, NY 14853, USA. 10Institute for Theoretical Physics, University of Amsterdam, Tyndall Avenue, 1090 . GL Amsterdam, the Netherlands 11Department of Physics, Ohio State University, Columbus, OH 43210, USA. A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunneling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude that impacts the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states. Correspondence and requests for materials should be addressed to U.C. ([email protected]) or S.R. ([email protected]) 1 The formation of charge-density waves (CDWs) and the CDW order parameter, which is proportional to the energy superconductivity are archetypical examples of symmetry gap Δ, and φ the phase of the CDW, i.e., the location of the breaking in materials, which are characterized by a complex charge modulation with respect to the underlying lattice. It is order parameter. In clean weak-coupling systems, the formation straightforward to realize that there are two ways to destroy the of the amplitude and the establishment of macroscopic phase order parameter — (i) by reducing the amplitude ρ0 through coherence are known to occur simultaneously at the transition excitations across the energy gap and/or (ii) by randomization temperature1,2, but the situation may be dramatically different at of the phase φ either through thermal or quantum fluctuations. strong coupling or in the presence of disorder3-9. Such systems Similar to the case of BCS transitions in clean superconductors, generally exhibit short correlation lengths and a transition the expectation value of δρ in weakly coupled CDW systems temperature that is greatly suppressed from the expected mean- vanishes via (i), as, in general, (ii) is not relevant due to the field value. This opens the possibility for a gap in the electronic large magnitude of the phase stiffness energy1,3. However, spectra to persist in the absence of long-range order over a large strongly coupled CDW systems can be susceptible to strong temperature range and the opportunity to study this so-called phase fluctuations due to their shorter coherence lengths1,4-7. pseudogap behaviour, which has been observed in a wide range To explore this systematically as a function of disorder in a of systems from high-temperature superconductors10-12 to material with a simple electronic and crystal structure, we 13 14 disordered superconducting thin films and cold atoms , in a investigate pristine and intercalated (with Co and Mn ions) simple system. 2H-NbSe2 samples, where CDW ordering involves strong 15,16 In the CDW state below the transition temperature Tcdw, a electron-phonon coupling . In our investigations, we employ modulation appears in the density of conduction electrons that a combination of experimental probes. Scanning tunneling is accompanied by a periodic lattice distortion1. Although this microscopy (STM) and X-ray diffraction (XRD) are used to lattice distortion leads to an increase in the elastic energy, there is measure the real and momentum space structure of the CDW a net gain in the free energy of the system due to a reduction in order, respectively. Angle resolved photoemission spectroscopy the energy of the electrons via the opening of an energy gap Δ. (ARPES) is employed to investigate the presence of an energy The CDW state is characterized by the order parameter gap in the electronic spectra, which is proportional to the δρ(r) = ρ(r) - ρav(r) = ρ0 cos[q.r +φ(r)], where q is the CDW amplitude of the order parameter, and to infer the existence or wave vector, ρav the average charge density, ρ0 the amplitude of disappearance of phase coherence of the order parameter Figure 1 | CDW phase transition for pure and intercalated 2H-NbSe2 samples. (a) Intensity of the CDW superstructure peak as a function of T for an x=0 (green) and x=0.0045 (Mn-intercalated, red). Dotted lines are guides to the eye indicating the growth of the CDW order parameter. Arrows mark the estimated Tcdw, which is the interpolation of the linear part to zero. (b) FF divided EDCs for various temperatures at the momentum location shown by the red dot in Fig. 2d. (c) FF divided EDCs for different x at the lowest measured temperatures. The sample with x=0.0165 is intercalated with Co, the others are intercalated with Mn. The corresponding momentum location is shown by the pink dot in Fig. 2d. The red dashed line in b and c shows the energy location of the peak (for T< Tcdw & x<xc) and kink (for T>Tcdw or x>xc) in the EDCs, while the black line is the chemical potential. (d) Intensity profile of CDW superstructure peaks along (0,K,0) for x=0, 0.0045 (intercalated with Mn) at 1.5 K and for x=0 at T = 35 K. The intensities have been normalized to that of the (0,4,4) Bragg peak and have subsequently been multiplied by the factors displayed in the legend to make them all visible on the same scale. (e,f) Normalized spectral weight associated with the coherence peak, following the procedure as described below, as a function of T for x=0 and as a function of x at the lowest measured temperature. The black dots correspond to Tcdw for x=0 and xc ~ 0.013, respectively. For x=0, the coherent spectral weight was obtained as the remaining integrated spectral intensity after subtracting the highest measured temperature (60K) as background and dividing by the value obtained at the lowest measured temperature. We adopt the same procedure, as for the normalized spectral weight as a function of T, for its x dependence by considering the spectrum at the highest value of x as the background and dividing the coherent spectral weight at the lowest measured temperature for each x by the one for x=0. 2 through the presence or absence of sharp coherence peaks in the limited even at our lowest measured temperature. This suggests ARPES spectra. Furthermore, Tcdw is determined by tracking that the process of intercalation gives rise to disorder that the onset of the CDW order parameter in XRD and the CDW- impacts the CDW state, consistent with previous work on 19-22 induced anomaly in transport measurements. Our main results 2H-NbSe2 and other dichalcogenide systems . We can from this extensive set of measurements are as follows. First, nevertheless still identify a CDW transition temperature, even the temperature Tcdw, above which CDW phase coherence is in the intercalated, disordered samples, from a linear destroyed, is suppressed with intercalation x and vanishes at a extrapolation of the temperature dependence of the quantum phase transition (QPT) at xc. Second, the CDW state superstructure intensity, as indicated in Fig. 1a. below Tcdw(x) and x < xc has an energy gap and sharp electronic From our XRD data on samples with different concentrations x excitations. Finally, the CDW energy gap survives above of intercalant ions, we observe that Tcdw is quickly suppressed Tcdw(x) and x > xc in the state which has only short-range CDW (Fig. 1a) as x is increased and beyond xc, superstructure peaks correlations, but the electronic excitations are no longer well- become very broad, indicating that the CDW order becomes defined. short-range.Qualitatively, similar attributes have been identified in resistivity measurements as well: the CDW induced anomaly Results in the resistivity becomes weaker with increasing x, shifts to lower XRD and transport. Previous investigations of the CDW tran- temperatures and eventually disappears beyond xc (see ref. 22, sition in 2H-NbSe2 using neutron and XRD have shown that a Supplementary Note 1 and Supplementary Fig. 2). We note that superstructure with incommensurate wave vector q=(1-δ)a*/3, the effect of doping on the CDW is the same irrespective of where a*=4π/√3a, lattice parameter a=3.44 Å and δ∼0.02, whether the intercalating ion is Mn or Co as observed by STM, appears below Tcdw=33K (ref.
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